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Cosmological Constant and Planck Length in relativity

  1. Jul 7, 2009 #1
    There seems to be a difference in the way relativity views Planck length as frame dependent and the cosmological constant, an energy density?, as invariant....Any insights appreciated!

    There is a well known contradiction between relativity and the Planck length:

    Wikipedia explains the contradiction nicely:


    Yet the energy density of empty space is believed now to have a positive value and apparently this cosmological constant of "...universal energy density would have the same value for all observers, no matter where or when they made their observations no matter how they moved."

    (which is why Einstein called it "constant")

    Lee Smolin, THE TROUBLE WITH PHYSICS, 2006, P151.

    Or is the cosmological constant not quite like an energy density??
    Last edited: Jul 7, 2009
  2. jcsd
  3. Jul 7, 2009 #2


    Staff: Mentor

    I have heard this argument before, but it is not a sound argument and if there really is a contradiction this is not the reason.

    Quantum Gravity would be the physical law which would apply at all scales. That one observer would be able to take one limit of QG and another observer would not be able to take the same limit is not a contradiction in any sense.

    The same thing applies in SR where an observer at rest wrt some system could use Newtonian physics and an observer moving at relativistic velocities wrt the same system would need to use SR. In both cases SR is the "same physical law" used to describe the situation in each frame, Newtonian physics being simply a limiting case of SR.
  4. Jul 7, 2009 #3
    Well there ARE different versions of double special relativity; wikipedias reflects the original via Giovanni Camelia; Lee Smolin and collaborators produced another....so saying

    may be your opinion, but well respected theoretical physicsts disagree. I sure don't know any resolution hence this post

    Maybe this IS a contradiction and there are NO answers yet.

    Even so, how does the cosmological constant stay invariant that way in relativity??
  5. Jul 7, 2009 #4


    Staff: Mentor

    Appeal to authority is a logical fallacy. The argument is valid or not valid regardless of who uses it.

    I should put a caviat in my previous reply, that is that I am assuming that a correct Quantum Gravity theory would be Lorentz symmetric, like other Quantum Field Theories.
    Last edited: Jul 7, 2009
  6. Jul 7, 2009 #5


    User Avatar
    Science Advisor

    It is proportional to the metric.
    IOW: It's not simply an energy density, there are also pressure terms that make it invariant.
  7. Jul 8, 2009 #6
    Ich...Thank you!

    (I wonder where Einstein got the idea to put pressure in GR?? Smart, very smart!!)
    Last edited: Jul 9, 2009
  8. Jul 9, 2009 #7
    My guess is that the density term is precisely equal to the 3P/c^2 term where P is negative - leaving only the cosmological term as driving the expansion (a la de Sitter).
  9. Jul 9, 2009 #8
    pressure of the vacuum (given it has energy density)
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